Coulomb screening in graphene with topological defects

We analyze the screening of an external Coulomb charge in gapless graphene cone, which is taken as a prototype of a topological defect. In the subcritical regime, the induced charge is calculated using both the Green’s function and the Friedel sum rule. The dependence of the polarization charge on the Coulomb strength obtained from the Green’s function clearly shows the effect of the conical defect and indicates that the critical charge itself depends on the sample topology. Similar analysis using the Friedel sum rule indicates that the two results agree for low values of the Coulomb charge but differ for the higher strengths, especially in the presence of the conical defect. For a given subcritical charge, the transport cross-section has a higher value in the presence of the conical defect. In the supercritical regime we show that the coefficient of the power law tail of polarization charge density can be expressed as a summation of functions which vary log periodically with the distance from the Coulomb impurity. The period of variation depends on the conical defect. In the presence of the conical defect, the Fano resonances begin to appear in the transport cross-section for a lower value of the Coulomb charge. For both sub and supercritical regime we derive the dependence of LDOS on the conical defect. The effects of generalized boundary condition on the physical observables are also discussed.     

Echoes of relativistic Landau levels in graphene and bilayer graphene

The problem of echo effects that can originate in graphene and bilayer graphene upon the generation of relativistic Landau levels in a quantizing magnetic field is considered. Graphene (bilayer graphene) is considered in a long-wave approximation near the Dirac points. It is proposed that the echo effect be used for the quantum memory of optical states in the far infrared.     

Collapse of Landau levels in gated graphene structures

We describe a new regime of magnetotransport in two-dimensional electron systems in the presence of a narrow potential barrier. In such systems, the Landau level states, which are confined to the barrier region in strong magnetic fields, undergo a deconfinement transition as the field is lowered. Transport measurements on a top-gated graphene device are presented. Shubnikov-de Haas (SdH) oscillations, observed in the unipolar regime, are found to abruptly disappear when the strength of the magnetic field is reduced below a certain critical value. This behavior is explained by a semiclassical analysis of the transformation of closed cyclotron orbits into open, deconfined trajectories.     

Landau levels in a simple hexagonal bilayer graphene

A new approach, which makes the Hamiltonian of the Peierls tight-binding model change into a band matrix, is used to investigate the Landau levels in a AA-stacked bilayer graphene. The interlayer atomic hoppings could induce an energy gap, the asymmetry of the Landau levels about the chemical potential, the random variation in the level spacing, more fourfold degenerate Landau levels at low energy, and the oscillatory Landau levels and the complicated state degeneracies at moderate energy. For the low-energy Landau levels, their dependence on the quantum number and the field strength cannot be well characterized by a simple power law. They exhibit a anomalous oscillation during the variation of the magnetic field. The main features of the magnetoelectronic states are directly reflected in density of states.     

Infrared spectroscopy of Landau levels of graphene

We report infrared studies of the Landau level (LL) transitions in single layer graphene. Our specimens are density tunable and show in situ half-integer quantum Hall plateaus. Infrared transmission is measured in magnetic fields up to B=18 T at selected LL fillings. Resonances between hole LLs and electron LLs, as well as resonances between hole and electron LLs, are resolved. Their transition energies are proportional to sqrt[B], and the deduced band velocity is (-)c approximately equal to 1.1 x 10(6) m/s. The lack of precise scaling between different LL transitions indicates considerable contributions of many-particle effects to the infrared transition energies.     

Novel electric field effects on Landau levels in graphene

A new effect in graphene in the presence of crossed uniform electric and magnetic fields is predicted. Landau levels are shown to be modified in an unexpected fashion by the electric field, leading to a collapse of the spectrum, when the value of electric to magnetic field ratio exceeds a certain critical value. Our theoretical results, strikingly different from the standard 2D electron gas, are explained using a "Lorentz boost," and as an "instability of a relativistic quantum field vacuum." It is a remarkable case of emergent relativistic type phenomena in nonrelativistic graphene. We also discuss few possible experimental consequence.     

The modulation effects on Landau levels in graphene nanoribbon

Magnetic-modulation effects in one-dimensional graphene nanoribbon have been investigated by the Peierls tight-binding model. The energy dispersion exhibits unusual oscillatory behavior which is mainly dominated by the modulation strength, the period, and the ribbon width. The main features of energy band are directly reflected in density of states, such as the structure, the height, the position, and the number of prominent peaks.     

Landau levels in graphene in the presence of emergent gravity

We consider graphene in the presence of external magnetic field and elastic deformations that cause emergent magnetic field. The total magnetic field results in the appearance of Landau levels in the spectrum of quasiparticles. In addition, the quasiparticles in graphene experience the emergent gravity. We consider the particular choice of elastic deformation, which gives constant emergent magnetic field and vanishing torsion. Emergent gravity may be considered as perturbation. We demonstrate that the corresponding first order approximation affects the energies of the Landau levels only through the constant renormalization of Fermi velocity. The degeneracy of each Landau level receives correction, which depends essentially on the geometry of the sample. There is the limiting case of the considered elastic deformation, that corresponds to the uniformly stretched graphene. In this case in the presence of the external magnetic field the degeneracies of the Landau levels remain unchanged.     

Landau levels in deformed bilayer graphene at low magnetic fields

We review the effect of uniaxial strain on the low-energy electronic dispersion and Landau level structure of bilayer graphene. Based on the tight-binding approach, we derive a strain-induced term in the low-energy Hamiltonian and show how strain affects the low-energy electronic band structure. Depending on the magnitude and direction of applied strain, we identify three regimes of qualitatively different electronic dispersions. We also show that in a weak magnetic field, sufficient strain results in the filling factor ν=±4 being the most stable in the quantum Hall effect measurement, instead of ν=±8 in unperturbed bilayer at a weak magnetic field. To mention, in one of the strain regimes, the activation gap at ν=±4 is, down to very low fields, weakly dependent on the strength of the magnetic field.     

Landau levels in uniaxially strained graphene: A geometrical approach

The effect of strain on the Landau levels (LLs) spectra in graphene is studied, using an effective Dirac-like Hamiltonian which includes the distortion in the Dirac cones, anisotropy and spatial-dependence of the Fermi velocity induced by the lattice change through a renormalized linear momentum. We propose a geometrical approach to obtain the electron’s wave-function and the LLs in graphene from the Sturm–Liouville theory, using the minimal substitution method. The coefficients of the renormalized linear momentum are fitted to the energy bands, which are obtained from a Density Functional Theory (DFT) calculation. In particular, we evaluate the case of Dirac cones with an ellipsoidal transversal section resulting from uniaxially strained graphene along the Arm-Chair (AC) and Zig-Zag (ZZ) directions. We found that uniaxial strain in graphene induces a contraction of the LLs spectra for both strain directions. Also, is evaluated the contribution of the tilting of Dirac cone axis resulting from the uniaxial deformations to the contraction of the LLs spectra.     

Scattering of charge carriers in graphene induced by topological defects

We study the scattering of graphene quasiparticles by topological defects, represented by holes, pentagons and heptagons. For holes, we found that at low concentration they give a negligible contribution to the resistivity. Whenever pentagons or heptagons are introduced we realize that a fermionic current is scattered by defects.     

Landau quantization for an induced electric dipole in the presence of topological defects

In this contribution we investigate the non-relativistic quantum dynamics of induced electric dipoles in the presence of a topological defect. We propose an analog of Landau quantization for neutral atoms, where a electric dipole is induced by the electromagnetic field configuration. We investigate this system in the presence of a topological defect and show that it breaks the infinite degeneracy of Landau levels.     

Electric- and magnetic-field-tuned Landau levels and Hall conductivity in AA-stacked bilayer graphene

We theoretically study the combined effect of magnetic and electric fields on the Landau levels and Hall conductivity in AA-stacked bilayer graphene. From the analytic expressions derived, we obtain explicit criterions for determining the zero-energy Landau level and different level crossings in the graphene bilayer. For providing a scheme of experimental verification, we further explore the quantum Hall effect in such a biased bilayer. It is found that the zero-conductance Hall plateau in this system can vanish at certain specific combinations of magnetic and electric fields, accompanying with the occurrence of resonance Hall conductivity steps.     

The linewidth of infrared light transitions between the Landau levels in graphene

We theoretically propose a structure that the population inversion between the Landau levels (LLs) of the graphene can be achieved by the electrical injection. This structure may be used for the Landau level-laser and related infrared and terahertz emitters. We mainly study the linewidth of the optical transitions between LLs in graphene due to the electron–acoustic phonon scattering. Within the Huang–Rhysʼs lattice relaxation model, we improve the effective single-phonon mode (ESM) for the acoustic phonon to calculate the linewidth of the optical transition and compare the obtained results with that of in the low and high-temperature limit. We find that the ESM provides a very good approximation for the temperature dependence of linewidth, which covers the dominating features of the low and high-temperature limit.     

Localized vibrational,edges and breathing modes of graphene nanoribbons with topological line defects

Peculiar vibrational modes of graphene nanoribbons (GNRs) with topological line defects were presented. We find that phonon dispersion relations of the topological defective GNRs are more similar to those of perfect armchair-edge GNR than to zigzag-edge GNR in spite of their zigzag edge. All vibrational modes at Γ point are assigned in detail by analyzing their eigenvectors and are presented by video. Three types of characteristic vibrational modes, namely, localized vibrational modes in defect sites, edges, and breathing modes, are observed. Five localized vibrational modes near the defect sites are found to be robust against the width of the topological line-defective GNR. The Raman D’ band just originates from one localized mode, 1622 cm^-1. The vibrational mode is sensitive to symmetry. The edge modes are related with structural symmetry but not with widths. Two edge modes are asymmetrical and only one is symmetrical. The breathing modes are inversely proportional to the width for wide-defect GNRs, and inversely proportional to the square root of the width for narrow-defect GNRs. The breathing mode frequencies of defective GNRs are slightly higher than those of perfect GNRs. These vibrational modes may be useful in the manipulation of thermal conductance and implementation of single phonon storage.     

Hydrogen adsorption and storage of Ca-decorated graphene with topological defects: A first-principles study

As a candidate for hydrogen storage medium, geometric stability and hydrogen capacity of Ca-decorated graphene with topological defects are investigated using the first-principle based on density functional theory (DFT), specifically for the experimentally realizable single carbon vacancy (SV), 585 double carbon vacancy (585 DCV) and 555–777 double carbon vacancy (555–777 DCV) defects. It is found that Ca atom can be stabilized on above defective graphenes since Ca׳s binding energy on vacancy defect is much larger than its cohesive energy. Up to six H₂ molecules can stably bind to a Ca atom on defective graphene with the average adsorption energies of 0.17–0.39 eV/H₂. The hybridization of the Ca-3d orbitals with H₂-σorbitals and the electrostatic interaction between the Ca cation and the induced H₂ dipole both contribute to the H₂ molecules binding. Double-side Ca-decorated graphene with 585 DCV and 555–777 DCV defects can theoretically reach a gravimetric capacity of 5.2 wt% hydrogen, indicating that Ca-decorated defective graphene can be used as a promising material for high density hydrogen storage.     

Diffusion, coalescence, and reconstruction of vacancy defects in graphene layers

Diffusion, coalescence, and reconstruction of vacancy defects in graphene layers are investigated by tight-binding molecular dynamics (TBMD) simulations and by first principles total energy calculations. It is observed in the TBMD simulations that two single vacancies coalesce into a 5-8-5 double vacancy at the temperature of 3000 K, and it is further reconstructed into a new defect structure, the 555-777 defect, by the Stone-Wales type transformation at higher temperatures. First principles calculations confirm that the 555-777 defect is energetically much more stable than two separated single vacancies, and the energy of the 555-777 defect is also slightly lower than that of the 5-8-5 double vacancy. In TBMD simulation, it is also found that the four single vacancies reconstruct into two collective 555-777 defects which is the unit for the hexagonal haeckelite structure proposed by Terrones et al. [Phys. Rev. Lett. 84, 1716 (2000)].     

Brownian motion in crystals with topological defects

The diffusion behaviour of a Brownian particle in a crystal with randomly distributed topological defects is analyzed by means of the continuum theory of defects combined with the theory of diffusion on manifolds. A path-integral representation of the diffusion process is used for the calculation of cumulants of the particle position averaged over a defect ensemble. For a random distribution of disclinations the problem of Brownian motion reduces to a known random-drift problem. Depending on the properties of the disclination ensemble, this yields various types of subdiffusional behaviour. In a random array of parallel screw dislocations one finds a normal, but anisotropic, diffusion behaviour of the mean-square displacement. Moreover, the process turns out to be non-Gaussian, and reveals long-time tails in the higher-order cumulants.Dedicated to Professor Herbert Wagner on the occasion of his 60th birthday     

Landau levels in disordered alloys

The electronic structure of a substitutionally disordered alloy in a uniform magnetic field has been studied on a simple model of scattering potentials (zero range potentials). The coherent potential and single-site aproximation have been employed. It turned out that in wide energy region the Dingle temperature, characterizing the decay of the amplitude of de Haas — van Alphen oscillations, is determined by the part of self-energy which does not depend on magnetic field. The field dependent part is important only for a few Landau levels at the bottom of the band. The results can be applied to simple metals and semi-metals.